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Literary claims to ownership of the third culture of sociology are considered and the rise of scientific method traced. The institutional history is summarized from the establishment of a chair of sociology at the London School of Economics and Political Science in 1907. Phases of expansion (1950–67), revolt (1968–75) and uncertainty (1976–2000) are described. Analysis of the professors—their origins, careers and fame—is presented. A content analysis of three leading British journals of sociology is reported. An epilogue is finally added of eight essays by well‐known sociologists—A. H. Halsey, Z. Bauman, C. Crouch, A. Giddens, A. Oakley, J. Platt, W.G. Runciman, and J. Westergaard.

This paper advances the position that sociology needs to develop an approach to research which focuses on fundamental social problems. In doing so it shares many of the intellectual values and goals of political arithmetic while seeking to move methodologically beyond it. Since such problems are complex they will require, typically, interdisciplinary input and a concomitant approach to the development and appraisal of theories. We are not, therefore, advocating the primacy of sociology but arguing that it has a distinctive part to play in addressing the fundamental problems of the twenty-first century. However, a policy-oriented sociology has also to take up the task, so clearly defined by the tradition of political arithmetic, which is to hold governments to account. Consequently a central principle of a new policy science is that it should contribute to democratic debate about policy.

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